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SCIENCE. 



[N. S. Vol. XIX. No. 478. 



analytic geometry down to the last index 

 and subscript, or, on the other hand, when 

 the devotee of a cult toasts his favorite sub- 

 ject with the words 'Here's to the higher 

 mathematics, may they never be useful. ' 



To the workaday world the higher ranges 

 of mathematics have been a sealed book; 

 the man who traverses them successfully 

 a magician — a man whose mental occupa- 

 tions awaken mingled feelings of awe and 

 pity, awe that he can soar so high, pity that 

 he wastes his strength in such useless flight. 

 A generation ago the mathematician was 

 joined in hand with the Roman and the 

 Greek, and the three easily persuaded the 

 educational world that they were the di- 

 vine trio. Without them for a basis there 

 could be nothing but a sham college course. 

 Why it was that these three lines of study 

 held such a commanding and, for the most 

 part, unchallenged position, it is now diffi- 

 cult for us to say. Possibly they gained 

 higher esteem as means of mental disci- 

 pline because their most ardent votaries 

 so seldom succeeded in making them di- 

 rectly useful except in certain narrow pro- 

 fessional lines. Of the men in college 

 courses who studied required mathematics 

 beyond trigonometry very few gained any 

 vital conception of analytic geometry and 

 the calculus. To most collegians the mass 

 of symbols with which they juggled in pur- 

 suing these subjects was a distressing night- 

 mare, a matter of jest and to be forgotten 

 with all possible speed. 



Our colleges to-day have seen a great 

 light and have reformed their curricula. 

 They now know there is no discipline in the 

 pursuit of mathematics to the man who 

 does not understand its language. Early 

 in his course, if not throughout it, the stu- 

 dent is allowed the more rational way of 

 getting his education, by pursuing subjects 

 that he can understand. This sensible treat- 

 ment of educational material has grown up 

 during the development of technical col- 



leges and may be referred in a measure at 

 least to their influence. Certainly great ad- 

 vance in the teaching of mathematics has 

 recently been made, yet very much remains 

 to be done, and the next great forward 

 movement seems to be coming directly from 

 the engineers and the forces they are setting 

 in operation. 



The literature on the question of reform 

 in the teaching of mathematics is growing 

 rapidly. In 1901 John Perry, professor 

 of mechanics and mathematics of the Royal 

 College of Science, London, and chairman 

 of the Board of Examiners of the Board 

 of Education in Engineering and Mathe- 

 matics, produced a profound impression 

 upon the British Association by a paper 

 on 'The Teaching of Mathematics.' His 

 ideas require attention further along. In 

 Germany Nernst and Schoenflies, for ex- 

 ample, have met the thought of the hour 

 in their 'Einfiihring in die Mathematische 

 Behandlung der Naturwissenchaften. ' In 

 our own country Perry centers are spring- 

 ing up for the reformation and profound 

 improvement, if not revolution, of mathe- 

 matical teaching in our secondary schools. 

 In the west the apostle of this movement is 

 Professor E. H. Moore, of Chicago Univer- 

 sity. One needs only to read his admirable 

 presidential address before the American 

 Mathematical Society in New York almost 

 exactly a year ago to understand the full 

 meaning and extent of the changes sought. 



The address will be found in the num- 

 ber of the Bulletin of the American Mathe- 

 matical Society for last May, and it will 

 repay a careful perusal on the part of those 

 of you who have not read it. Professor 

 Moore has been counted as a pure mathe- 

 matician of the most pronounced type, but 

 into this new movement he has thrown him- 

 self with the ardor of one whose whole life 

 had been spent in applying a wide range of 

 mathematical power to the design and con- 

 struction of the great objects of engineer- 



